A number n with k digits and digit sum s occurs in the sequence if and only if (10^k-1)*s = 9*k*n. [From Hagen von Eitzen, Jun 17 2009]

Many terms (perhaps all) are related to decimal expansions of fractions with a power of 3 in the denominator (see Munafo webpage) [From Robert Munafo, Jun 18 2009]

Replacing "all possible permutations" in the definition with "all cyclic permutations" produces the same sequence. Even more generally, the symmetric group can be replaced by any finite group operating transitively on the n places. [From Hagen von Eitzen, Jun 22 2009]